Pure O-sequences and matroid h-vectors

We study Stanley's long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley's conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley's conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators.Comment: Contains several changes/updates with respect to the previous version. In particular, a discussion of a possible approach to the general case is included at the end. 13 pages. To appear in the Annals of Combinatoric

Nerve sheath catheter analgesia for forequarter amputation in paediatric oncology patients

In a single centre over two years, four children (7 to 10 years old) with upper limb osteosarcoma underwent chemotherapy followed by forequarter amputation. All patients had preoperative pain and were treated with gabapentin. Nerve sheath catheters were placed in the brachial plexus intraoperatively and left in situ for five to 14 days. After surgery, all patients received local anaesthetic infused via nerve sheath catheters as part of a multimodal analgesia technique. Three of the four patients were successfully treated as outpatients with the nerve sheath catheters in situ. All four children experienced phantom limb pain; however, it did not persist beyond four weeks in any patient.R. N. Kaddoum, L. L. Burgoyne, L. A. Pereiras, M. Germain, M. Neel, D. L. Anghelesc

Long-term use of nerve block catheters in paediatric patients with cancer related pathologic fractures

We report three cases of children with osteosarcoma and pathologic fractures treated with long-term continuous nerve blocks for preoperative pain control. One patient with a left distal femoral diaphysis fracture had a femoral continuous nerve block catheter for 41 days without complications. Another with a fractured left proximal femoral shaft had three femoral continuous nerve block catheters for 33, 26 and 22 days respectively. The third patient, whose right proximal humerus was fractured, had a brachial plexus continuous nerve block catheter for 36 days without complication. In our experience, prolonged use of continuous nerve block is safe and effective in children with pathologic fractures for preoperative pain control.L. L. Burgoyne, L. A. Pereiras, L. A. Bertani, R. N. Kaddoum, M. Neel, L. G. Faughnan, D. L. Anghelesc